Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
570 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C9×C4⋊C4 | C2 | semidirect |
| 3. #11720571 | C2 | semidirect |
| 4. #11720528 | C2 | semidirect |
| 5. #11720526 | C2 | semidirect |
| 22. C2×C9×C4⋊C4 | D3 | semidirect |
| 69. C2×C3×C4⋊C4 | D9 | semidirect |
| 148. C2×C4⋊C4 | C3⋊D9 | semidirect |
| 152. C3×C9 | #481 | semidirect |
| 217. C9 | #4968 | semidirect |
| 250. C3 | #10588651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×C4⋊C4 | 2 |
| #11721819 | 2 |
| #11720571 | 2 |
| #11720528 | 2 |
| #11720526 | 2 |
| #10592667 | 3 |
| #10588651 | 3 |